A229131 Numbers k such that the distance between the k-th triangular number and the nearest square is exactly 1.

1, 2, 4, 5, 15, 25, 32, 90, 148, 189, 527, 865, 1104, 3074, 5044, 6437, 17919, 29401, 37520, 104442, 171364, 218685, 608735, 998785, 1274592, 3547970, 5821348, 7428869, 20679087, 33929305, 43298624

Offset

1,2

Comments

The k-th triangular number (A000217(k)) is a square plus or minus one.

Union of A006451 (k-th triangular number is a square minus one) and A072221 (k-th triangular number is a square plus one).

Links

Table of n, a(n) for n=1..31.

Formula

G.f.: (-x^7 + 2*x^6 - 2*x^5 + 4*x^4 - 5*x^3 + 2*x^2 + x + 1)/((1-6*x^3+x^6)*(1-x)) (conjectured).

Example

A000217(4)=10 and 10 - 3^2 = 1 so 4 is in the sequence.
A000217(5)=15 and 4^2 - 15 = 1 so 5 is in the sequence.

Prog

(PARI) for(n=1, 10^8, for(i=-1, 1, f=0; if(i&&issquare(n*(n+1)/2+i), f=1; break)); if(f, print1(n, ", ")))

Crossrefs

Cf. A000217, A001110, A006451, A072221, A229083, A229118.

Sequence in context: A178436 A370959 A328230 * A359050 A071316 A056401

Adjacent sequences: A229128 A229129 A229130 * A229132 A229133 A229134

Keyword

nonn

Author

Ralf Stephan, Sep 15 2013

Status

approved